CN108416445B - Design method for quantum real signal storage and quantum circuit realization - Google Patents
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Abstract
The invention provides a storage design method of quantum real signals and quantum circuit realization, and belongs to the field of quantum signal processing. The invention designs a quantum 2-dimensional real signal storage method and a quantum 2-dimensional three-channel real signal storage method by adopting tensor products and quantum superposition states; and a circuit for realizing quantum 2-dimensional real signal storage and a circuit for realizing quantum 2-dimensional three-channel real signal storage are designed. The invention solves the problem of how to store real signals in a quantum system, provides necessary foundation for subsequent quantum signal processing, embodies that the quantum information processing is superior to the traditional signal processing in the aspect of signal storage, and has great significance for the perfection of quantum computing theory and the popularization of application.
Description
Technical Field
The invention relates to the field of quantum signal processing, in particular to a storage design method of quantum real signals and a quantum implementation circuit.
Background
The quantum signal processing is a product of combining quantum computing and signal processing technologies, and the parallelism and the superposition of the quantum computing are the basis of the quantum signal processing superior to the classical signal processing.
In quantum computing, an information element is represented by a qubit, having two fundamental quantum states |0> and |1>, the fundamental quantum states being referred to simply as the ground states. A qubit can be a linear combination of two ground states, often referred to as a superposition state, which can be expressed as | ψ > ═ a |0> + b |1>, where a and b are two complex numbers.
Tensor products are a method of combining small vector spaces together to form a larger vector space, using symbols
And (4) showing. For quantum state | X>,|Y>Can be expressed as:
the n-times tensor product for quantum state | X > can be expressed as:
a quantum wire may be composed of a sequence of qubit gates, each line representing a connection of the quantum wire in the representation of the quantum wire, the sequence of execution of the quantum wire being from left to right. The qubit gates can be conveniently represented in matrix form, and the single qubit gate can be represented by a 2 x 2 unitary matrix U, i.e. U+U is I, wherein U+Is the conjugate transpose of U and I is the unit matrix. X (NOT gate), H (Hadamard gate) and
are three single-quantum-bit gates,
is the product of the n tensors of I. The names, symbols and corresponding matrix representations of some basic qubit gates are shown in fig. 1. The most important multi-qubit gate is the controlled U-gate, which is represented by a black dot when the control bit is 1 and a white dot when the control bit is 0, and the name and symbol of the controlled U-gate are shown in fig. 2. The right part in fig. 2 is an equivalent representation of the left part, and
according to the IEEE 754 international standard, the specification of 32-bit single-precision floating-point real numbers is shown in table 1. In table 1, sign bit 0 represents a positive number, 1 represents a negative number, ± ∞ represents positive and negative infinity, and NaN represents not a number.
Table 132 bit single precision floating point real number
| Sign bit | Step code (8 bit) | Mantissa (23 bits) | |
| 0 or 1 | 0 | 0 | ±0 |
| 0 or 1 | 0 | Binary number m different from 0 | ±0.m×2-126 |
| 0 or 1 | k(1≤k≤254) | Binary number m | ±1.m×2k-127 |
| 0 or 1 | 255 | 0 | ±∞ |
| 0 or 1 | 255 | Number other than 0 | NaN |
Disclosure of Invention
The invention provides a storage design method of quantum real signals, which comprises a quantum 2-dimensional real signal storage design, a quantum 2-dimensional three-channel real signal storage design and a corresponding quantum realization circuit, solves the technical problem that the existing storage method can not store real signals in a quantum system, and simultaneously solves the problem that the traditional storage method needs a large memory, so that the quantum storage of the real signals is realized, and a basic support is provided for other quantum signal processing operations.
The invention solves the problems through the following technical scheme:
the invention designs the single-precision floating-point number representation method of the quantum real signal according to the IEEE 754 international standard by fully utilizing the unique performances of quantum computation such as quantum parallelism, quantum superposition and the like, and constructs the quantum realization circuit of the storage design of the quantum real signal by utilizing the quantum controlled gate and the single-quantum bit gate.
The specific design scheme and steps of the invention are as follows:
a quantum real signal storage and quantum circuit realization design method, the method adopts tensor product and quantum superposition state design quantum 2 dimension real signal storage method and quantum 2 dimension three channel real signal storage method; designing a quantum 2-dimensional real signal storage realization circuit according to a quantum 2-dimensional real signal storage method; and designing a quantum circuit for storing the real signals of the quantum 2-dimensional three-channel according to the real signal storage method of the quantum 2-dimensional three-channel.
In the above scheme, it is preferable that the quantum 2-dimensional real signal storage method is implemented as follows:
storing a single precision floating point number with a 32 qubit quantum state:
wherein | S (x, y)>＝|Sxy>The sign bit of the bit is stored and,
the order code is stored in a memory of the mobile terminal,
storing mantissas, Sxy,
v, x and y are positive numbers;
the storage of the quantum 2-dimensional real signal is represented as
Wherein | l (x, y)>Representing the real value of the signal at position (x, y) | x>Representing the x-coordinate, | y of the signal>Representing the y-coordinate of the signal, the magnitude of the signal being 2n-k×2kAnd k and n are positive integers.
In the above scheme, it is preferable that the implementation circuit design process of the storage of the quantum 2-dimensional real signal is as follows:
the quantum implementation circuit of the quantum 2-dimensional real signal storage design is shown in fig. 3, and the schematic diagram is shown in fig. 4. In FIG. 3, the 0 th virtual frame implementation
Where I and H are a quantum unit gate and a Hardmard gate respectively,
is a quantum operation symbol;
u in FIG. 3s,UeAnd UmIs NOT gate or unit gate, and is defined as follows
Wherein I and X are a quantum unit gate and a quantum not gate respectively,
is the XOR operation symbol, | S (x, y)>＝|Sxy>The sign bit of the bit is stored and,
the order code is stored in a memory of the mobile terminal,
storing mantissas, Sxy,
v, x and y are positive numbers;
will Us,UeAnd UmFor quantum state |0 respectively>Operation is as follows
When t is 0nAt time-1, the (t +1) th virtual box implementation in FIG. 3
Therefore, quantum circuit design of quantum 2-dimensional real signal storage is realized.
In the above scheme, a quantum 2-dimensional three-channel real signal storage method is preferred:
the storage of the quantum 2-dimensional three-channel real signal is represented as
Wherein
Each storing a 2-dimensional real signal, i.e.
Here, | l1(x,y)>,|l2(x,y)>,|l3(x,y)>Representing the real values of the three channels of the signal at positions (x, y) | x>Representing the x-coordinate, | y of the signal>Representing the y-coordinate of the signal, the magnitude of the signal being 2n-k×2kK and n are positive integers;
the quantum implementation circuit of the quantum 2-dimensional three-channel real signal storage design is shown in fig. 5. In the context of figure 5, it is shown,
gates are shown in fig. 1, and controlled not gates and controlled H gates are shown in fig. 2, where not gates X and H are two specific U gates, and QRDS is a shorthand line for quantum 2-dimensional real signal storage.
In the above scheme, it is preferable that the quantum line implementation process of the quantum 2-dimensional three-channel real signal storage is as follows: and realizing the circuit realization of the quantum 2-dimensional three-channel real signal storage according to the circuit realization of the quantum 2-dimensional three-channel real signal storage and the quantum 2-dimensional real signal storage.
The invention has the advantages and effects that:
the invention solves the problem of how to store the real signal in the quantum system, and provides a necessary basis for subsequent quantum signal processing. The invention embodies that the quantum information processing is superior to the traditional signal processing in the aspect of signal storage: the quantum 2-dimensional real signal storage method uses n +32 quantum bits to store a quantum with the size of 2nThe real signal of (a); the quantum 2-dimensional three-channel real signal storage method uses n +34 quantum bits to store a signal with the size of 3 multiplied by 2nThe real signal of (2).
Drawings
FIG. 1 is a representation of a basic quantum gate of the present invention;
FIG. 2 is a representation of a multi-qubit gate of the present invention being a controlled U-gate;
FIG. 3 is a quantum implementation circuit diagram of the quantum 2-dimensional real signal storage method of the present invention;
FIG. 4 is a simplified diagram of a quantum implementation circuit diagram of the quantum 2-dimensional real signal storage method of the present invention;
FIG. 5 is a quantum implementation circuit diagram of the quantum 2-dimensional three-channel real signal storage method of the present invention;
FIG. 6 is a quantum implementation circuit diagram of an example of a quantum 2-dimensional real signal storage method of the present invention;
FIG. 7 is a simplified diagram of a quantum implementation circuit diagram of an example of a quantum 2-dimensional real signal storage method of the present invention;
fig. 8 is a quantum implementation circuit diagram of an example of the quantum 2-dimensional three-channel real signal storage method of the present invention.
Detailed Description
The present invention is further illustrated by the following examples.
Quantum 2-dimensional real signal storage design and quantum implementation circuit
Storing a single-precision floating-point number using a 32-qubit quantum state, i.e. storing a single-precision floating-point number
Wherein | S (x, y)>＝|Sxy>The sign bit of the bit is stored and,
the order code is stored in a memory of the mobile terminal,
storing mantissas, Sxy,
Further, the storage of the quantum 2-dimensional real signal is represented as
Wherein | l (x, y)>Representing the real value of the signal at position (x, y) | x>Representing the x-coordinate, | y of the signal>Representing the y-coordinate of the signal, signalHas a size of 2n-k×2kAnd k and n are positive integers.
When | l (x, y)>Quantum 2-dimensional real signal | ψ when an integer of 0 or more and 255 or less is stored2>And storing a gray scale image.
The quantum implementation circuit of the quantum 2-dimensional real signal storage design is shown in fig. 3, and the schematic diagram is shown in fig. 4. In FIG. 3, the 0 th virtual frame implementation
Wherein unit gates I and H are shown in figure 1,
is a quantum operation symbol.
Us,UeAnd UmThe definition is as follows:
wherein the unit gates I and X are as shown in figure 1,
is the sign of an XOR operation, Sxy,
Is a component of a floating point number, as shown in equation (1).
Will Us,UeAnd UmFor quantum state |0 respectively>Operation is as follows
When t is 0nAt time-1, the (t +1) th virtual box implementation in FIG. 3
Thus, the 1 st dotted box to the 2 nd dotted box in FIG. 3nThe virtual frames are continuously aligned with the quantum state | ψ in equation (3)>Operation to obtain
This illustrates that the quantum circuit in fig. 3 realizes quantum 2-dimensional real signal storage.
For example, a 22 X 2 real signal
Can be stored in the following quantum states:
the quantum implementation circuit is shown in fig. 6, and the simplified circuit is shown in fig. 7. In fig. 6, each dashed box enables the storage of a signal value at one coordinate.
Quantum 2-dimensional three-channel real signal storage design and quantum implementation circuit
The storage of the quantum 2-dimensional three-channel real signal is represented as
Wherein
Each storing a 2-dimensional real signal, i.e.
Here, | l1(x,y)>,|l2(x,y)>,|l3(x,y)>Representing the real values of the three channels of the signal at positions (x, y) | x>Representing the x-coordinate, | y of the signal>Representing the y-coordinate of the signal, the magnitude of the signal being 2n-k×2kAnd k and n are positive integers.
When l1(x,y)>,|l2(x,y)>,|l3(x,y)>When an integer greater than or equal to 0 and less than or equal to 255 is stored, respectively, the quantum 2-dimensional three-channel real signal | ψ3>And storing an RGB color image.
The quantum implementation circuit of the quantum 2-dimensional three-channel real signal storage design is shown in fig. 5. In the context of figure 5, it is shown,
gates are shown in fig. 1, and controlled not gates and controlled H gates are shown in fig. 2, where not gates X and H are two specific U gates, and QRDS is a shorthand line for quantum 2-dimensional real signal storage.
Corresponding to a real signal of three channels, assuming that signals of three channels are:
V1＝V2＝V3＝V (12)
wherein V1,V2,V3Respectively, the size of three channels is 22The real signal of x 2, V, is shown in equation (10).
This three-channel real signal can be stored in the following quantum states:
wherein | S2>As shown in equation (11), its quantum wires are shown in fig. 8. In the context of figure 8 of the drawings,
gates are shown in fig. 1, controlled not gates and controlled H gates are shown in fig. 2, when not gates X and H are two specific U gates, and line Q1 is shown in fig. 7.
While the preferred embodiments of the present invention have been described in detail, it is to be understood that the invention is not limited thereto, and that various equivalent modifications and substitutions may be made by those skilled in the art without departing from the spirit of the present invention and are intended to be included within the scope of the present application.
Claims (4)
1. A quantum real signal storage and quantum circuit realization design method is characterized in that a quantum 2-dimensional real signal storage method and a quantum 2-dimensional three-channel real signal storage method are designed by adopting tensor products and a quantum superposition state; designing a quantum 2-dimensional real signal storage realization circuit according to a quantum 2-dimensional real signal storage method; designing a quantum circuit for real signal storage of the quantum 2-dimensional three-channel according to a real signal storage method of the quantum 2-dimensional three-channel;
the quantum 2-dimensional real signal storage method is realized by the following steps:
storing a single precision floating point number with a 32 qubit quantum state:
wherein | S (x, y)>＝|Sxy>The sign bit of the bit is stored and,
the order code is stored in a memory of the mobile terminal,
the mantissa is stored in a memory of the memory,
v, x and y are positive numbers;
the storage of the quantum 2-dimensional real signal is represented as
Wherein | l (x, y)>Representing the real value of the signal at position (x, y) | x>Representing the x-coordinate, | y of the signal>Representing the y-coordinate of the signal, the magnitude of the signal being 2n-k×2kAnd k and n are positive integers.
2. The method of claim 1, wherein the circuit design process for storing quantum real signals and realizing quantum circuit implementation is as follows:
first, it is realized by H gate
Where I and H are a quantum unit gate and a Hardmard gate respectively,
is a quantum operation symbol;
Us，Ueand UmThe definition is as follows:
wherein I and X are a quantum unit gate and a quantum not gate respectively,
is the XOR operation symbol, | S (x, y)>＝|Sxy>The sign bit of the bit is stored and,the order code is stored in a memory of the mobile terminal,
the mantissa is stored in a memory of the memory,
v, x and y are positive numbers;
will Us，UeAnd UmFor quantum state |0 respectively>Operation is as follows
The quantum state | psi > in formula (3) is successively operated by controlled NOT gates to obtain
Therefore, quantum circuit design of quantum 2-dimensional real signal storage is realized.
3. The method of claim 1, wherein the method comprises: the quantum 2-dimensional three-channel real signal storage method comprises the following steps:
the storage of the quantum 2-dimensional three-channel real signal is represented as
Wherein
Each storing a 2-dimensional real signal, i.e.
Here, | l1(x，y)>，|l2(x，y)>，|l3(x，y)>Representing the real values of the three channels of the signal at positions (x, y) | x>Representing the x-coordinate, | y of the signal>Representing the y-coordinate of the signal, the magnitude of the signalIs as small as 2n-k×2kK and n are positive integers;
by using
And the realization circuit of the gate, the controlled NOT gate, the controlled H gate and the quantum 2-dimensional real signal storage realizes the quantum 2-dimensional three-channel real signal storage.
4. The method of claim 3, wherein the method comprises: the quantum circuit realization process of the quantum 2-dimensional three-channel real signal storage is as follows: and realizing the circuit realization of the quantum 2-dimensional three-channel real signal storage according to the circuit realization of the quantum 2-dimensional three-channel real signal storage and the quantum 2-dimensional real signal storage.
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